Problem: Solve for $x$ and $y$ using elimination. ${-2x+5y = 35}$ ${-5x-4y = -61}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${-10x+25y = 175}$ $10x+8y = 122$ Add the top and bottom equations together. $33y = 297$ $\dfrac{33y}{{33}} = \dfrac{297}{{33}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-2x+5y = 35}\thinspace$ to find $x$ ${-2x + 5}{(9)}{= 35}$ $-2x+45 = 35$ $-2x+45{-45} = 35{-45}$ $-2x = -10$ $\dfrac{-2x}{{-2}} = \dfrac{-10}{{-2}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {-5x-4y = -61}\thinspace$ and get the same answer for $x$ : ${-5x - 4}{(9)}{= -61}$ ${x = 5}$